Evaluate simple expressions with variables (as tested) - Health Education Systems Admission Assessment HESI

What is the risk score for a patient who is 50 years old and weighs 75 kg?
Answer: 7.5 When you encounter formula-based problems on the HESI, success depends on carefully identifying each variable and substituting values step by step. This question tests your ability to convert units and apply a given formula accurately. Let's work through the risk score formula: $S = 2a + w - 10$ , where $a$ is age in decades and $w$ is weight in kg divided by 10. First, convert the patient's age to decades: 50 years ÷ 10 = 5 decades, so $a = 5$ . Next, calculate the weight variable: 75 kg ÷ 10 = 7.5, so $w = 7.5$ . Now substitute into the formula: $S = 2(5) + 7.5 - 10 = 10 + 7.5 - 10 = 7.5$ The correct answer is A) 7.5. Looking at the wrong answers: B) 75 likely comes from using the raw weight (75 kg) instead of dividing by 10. C) 97.5 probably results from using the raw age (50) instead of converting to decades: $2(50) + 7.5 - 10 = 97.5$ . D) 165 appears to use both raw values: $2(50) + 75 - 10 = 165$ . Each incorrect answer represents a common error in unit conversion or variable identification. Always read the formula definition carefully and convert units before substituting. On the HESI, these calculation problems often include answer choices that match common mistakes, so double-check your unit conversions and arithmetic to avoid these traps.
Using Young's Rule, what is the correct dose for a 6-year-old child if the adult dose is 150 mg?
Answer: 50 mg When you encounter pediatric dosage calculations on the HESI, you'll often see standardized formulas like Young's Rule. These questions test your ability to substitute values correctly and perform accurate calculations under pressure. Let's work through Young's Rule step by step. The formula is $D = \frac{a}{a+12} \times A$ , where you substitute the child's age (a = 6 years) and adult dose (A = 150 mg): $D = \frac{6}{6+12} \times 150 = \frac{6}{18} \times 150$ Simplifying the fraction: $\frac{6}{18} = \frac{1}{3}$ Therefore: $D = \frac{1}{3} \times 150 = 50 \text{ mg}$ Answer A (50 mg) is correct because it follows the proper mathematical steps and gives a logical pediatric dose that's significantly smaller than the adult dose. Answer B (150.3 mg) likely results from calculation errors, possibly adding instead of following the correct order of operations. Answer C (450 mg) suggests multiplying 150 by 3 instead of dividing by 3 - a common mistake when working with fractions. Answer D (1950 mg) appears to come from multiplying all the numbers together (6 × 12 × 150 ÷ something), completely misunderstanding the formula structure. Remember that pediatric doses should always be smaller than adult doses, so immediately eliminate any answer that equals or exceeds the adult dose. Also, double-check your fraction work - converting to decimals (6÷18 = 0.33) can help verify your calculation.
A ventilator setting is calculated using $V = 450 + 6w - 15(a - 20)$ where $w$ is patient weight in kg and $a$ is age in years. For a 35-year-old patient weighing 85 kg, what is the appropriate ventilator setting?
Answer: 735 mL per breath When you encounter ventilator calculation problems on the HESI, you're being tested on your ability to substitute values accurately into medical formulas and perform algebraic operations correctly. Let's work through this step-by-step using the given formula $V = 450 + 6w - 15(a - 20)$ with a 35-year-old patient weighing 85 kg. First, substitute the values: $w = 85$ and $a = 35$ . $V = 450 + 6(85) - 15(35 - 20)$ Following order of operations, calculate within parentheses first: $(35 - 20) = 15$ Then multiply: $6(85) = 510$ and $15(15) = 225$ Finally: $V = 450 + 510 - 225 = 735$ mL per breath Now let's examine why the other options are incorrect. Choice A (960 mL) likely results from adding instead of subtracting the age adjustment: $450 + 510 + 225 = 1185$ , though this doesn't match exactly. Choice B (810 mL) might come from miscalculating the age factor as $15 × 20 = 300$ instead of $15 × 15 = 225$ , giving $450 + 510 - 150 = 810$ . Choice C (885 mL) could result from forgetting to subtract 20 from the age before multiplying: $450 + 510 - 15(35) = 450 + 510 - 525 = 435$ , which also doesn't match exactly. For HESI math problems, always double-check your order of operations and be especially careful with parentheses and negative signs in medical formulas, as these are common sources of calculation errors.
What is the correct drip rate in drops per minute, rounded to the nearest whole number?
Answer: 42 gtt/min IV drip rate calculations are fundamental nursing skills that require careful unit conversion and formula application. When you encounter these problems, always identify your given values and ensure all units are consistent before calculating. Let's work through this step-by-step using the formula $D = \frac{V \times d}{t}$ . You have V = 1000 mL, d = 20 gtt/mL, and the time is 8 hours. The critical step is converting hours to minutes: 8 hours × 60 minutes/hour = 480 minutes. Now substitute into the formula: $D = \frac{1000 \text{ mL} \times 20 \text{ gtt/mL}}{480 \text{ minutes}} = \frac{20,000}{480} = 41.67 \text{ gtt/min}$ Rounded to the nearest whole number, this gives 42 gtt/min, making C correct. Looking at the wrong answers: A (10 gtt/min) likely results from calculation errors or using the wrong time value. B (40 gtt/min) represents incomplete rounding—students might stop at 41.67 and round down to 40 instead of properly rounding to 42. D (2500 gtt/min) occurs when students forget to convert hours to minutes, using 8 instead of 480 in the denominator. Remember the key strategy: always convert time units to minutes first, then apply the formula methodically. Double-check your unit conversions—this is where most errors occur in IV calculation problems on the HESI.
If the fixed cost is $50 and the variable cost is $15 per hour, what is the total cost to operate the equipment for an 8-hour shift?
Answer: $170 This question tests your ability to substitute values into a linear equation and perform basic arithmetic calculations—skills essential for healthcare professionals who must calculate dosages, costs, and other quantitative measures. You're given the formula $C = F + Vh$ where each variable represents a specific cost component. To find the total cost, substitute the given values: $F = 50$ , $V = 15$ , and $h = 8$ . This gives you $C = 50 + 15(8)$ . Following order of operations, multiply first: $15 \times 8 = 120$ . Then add the fixed cost: $50 + 120 = 170$ . The total cost is $170. Looking at the wrong answers: Choice A ( $73) likely comes from adding the fixed cost to the variable rate without considering the hours worked ($ $50 + 15 + 8 = 73$ $). This ignores that the variable cost must be multiplied by time. Choice B ( $120) represents only the variable costs ($ $15 \times 8 = 120$ $) while completely forgetting to add the fixed cost component. Choice D ( $520) appears to result from incorrectly adding all values together and then performing some multiplication ($ $50 + 15 + 8 = 73$ $, then perhaps multiplying by something), showing a fundamental misunderstanding of the formula structure. When working with cost formulas on the HESI, always identify what each variable represents before substituting values. Fixed costs remain constant regardless of usage, while variable costs change with the amount of activity. Double-check that you're following the correct order of operations: handle multiplication before addition.
The oxygen saturation level for a patient is modeled by $S = 98 - 0.5d - 0.2(h - 15)$ , where $d$ is the disease severity index and $h$ is hours since last treatment. If the disease severity index is 6 and the last treatment was 23 hours ago, what is the predicted oxygen saturation level?
Answer: 93.4% using the complete formula Substituting $d = 6$ and $h = 23$ : $S = 98 - 0.5(6) - 0.2(23 - 15) = 98 - 3 - 0.2(8) = 98 - 3 - 1.6 = 93.4$ %. Choice B incorrectly calculates $0.2(8)$ as $1.0$ . Choice C omits the time component entirely. Choice D incorrectly uses $h = 15$ in the calculation, making $(h - 15) = 0$ .
What is the patient's temperature in degrees Celsius, rounded to the nearest tenth?
Answer: 38.5°C Temperature conversion questions are common in healthcare settings, as you'll need to interpret vital signs recorded in different measurement systems. The key is carefully applying the conversion formula and following proper order of operations. To convert 101.3°F to Celsius, substitute into the formula $C = \frac{5}{9}(F - 32)$ . First, solve what's in parentheses: $101.3 - 32 = 69.3$ . Next, multiply by the fraction: $\frac{5}{9} \times 69.3 = \frac{346.5}{9} = 38.5$ . The patient's temperature is 38.5°C. Looking at the wrong answers: Choice A (24.3°C) likely results from incorrectly subtracting 32 after multiplying by 5/9, rather than following proper order of operations. Choice C (74.1°C) appears to come from forgetting to multiply by 5/9 entirely, just subtracting 32 from the Fahrenheit temperature. Choice D (124.7°C) suggests adding 32 instead of subtracting it, then multiplying by 5/9. For HESI temperature conversion problems, always work systematically: subtract 32 first (since it's in parentheses), then multiply by 5/9. Remember that normal body temperature ranges help you check your work—98.6°F equals 37°C, so a fever of 101.3°F should convert to something just above 37°C. If your calculated answer seems physiologically impossible (like 124.7°C), double-check your arithmetic and order of operations.
A patient's medication dosage is calculated using the formula $D = 15(w + 8) - 3a$ , where $D$ is the dosage in mg, $w$ is the patient's weight in kg, and $a$ is the patient's age in years. If a 45-year-old patient weighs 72 kg, what is the correct dosage?
Answer: 1065 mg Substituting $w = 72$ and $a = 45$ into the formula: $D = 15(72 + 8) - 3(45) = 15(80) - 135 = 1200 - 135 = 1065$ mg. Choice B incorrectly omits the age factor ( $-3a$ ). Choice C suggests rounding is needed when the calculation yields an exact integer. Choice D incorrectly adds the age factor instead of subtracting it.
What is the patient's total fluid intake in mL for the shift?
Answer: 930 mL Fluid intake calculations are fundamental in nursing practice for monitoring patient hydration status and preventing complications. When you encounter these problems, systematically identify each fluid source and apply the given formula. Using the formula $I = b + m + v$ , let's calculate each component: Beverage intake (b): Two 240 mL cups of water = $2 \times 240 = 480 \text{ mL}$ Meal fluids (m): Broth consumed = $150 \text{ mL}$ IV fluids (v): 75 mL/hr for 4 hours = $75 \times 4 = 300 \text{ mL}$ Total intake: $I = 480 + 150 + 300 = 930 \text{ mL}$ Answer choice A (465 mL) likely represents only the beverage intake plus meal fluids (480 + 150 = 630 mL), but even this calculation is incorrect. Answer choice B (690 mL) appears to miscalculate the IV portion, perhaps using 3 hours instead of 4 (480 + 150 + 60 = 690 mL). Answer choice C (705 mL) might result from incorrectly calculating one cup of water instead of two (240 + 150 + 300 = 690 mL), though this doesn't match exactly either. The correct answer is D (930 mL). Study tip: Always break fluid calculations into clear categories and double-check your multiplication, especially for IV rates over time. On the HESI, these problems test both your mathematical accuracy and understanding of different fluid sources in healthcare settings.
Using the approximation $\pi \approx 3$ , find the surface area of a cylindrical vial with a radius $r = 3$ cm and height $h = 10$ cm.
Answer: 234 cm² When you encounter cylinder surface area problems on the HESI, remember that the formula $A = 2\pi rh + 2\pi r^2$ represents two components: the curved side surface ( $2\pi rh$ ) plus the top and bottom circular faces ( $2\pi r^2$ ). Let's substitute the given values systematically. With $r = 3$ cm, $h = 10$ cm, and $\pi \approx 3$ : $A = 2\pi rh + 2\pi r^2$ $A = 2(3)(3)(10) + 2(3)(3)^2$ $A = 180 + 2(3)(9)$ $A = 180 + 54 = 234 \text{ cm}^2$ Choice A (54 cm²) represents only the area of the two circular ends ( $2\pi r^2 = 54$ ) — you'd get this if you forgot to include the curved surface area entirely. Choice B (180 cm²) gives you just the curved surface area ( $2\pi rh = 180$ ) — this happens when you forget to add the top and bottom faces. Choice C (216 cm²) is a calculation error, possibly from incorrectly computing $2\pi r^2$ or making an arithmetic mistake in the addition. Choice D (234 cm²) correctly includes both surface components. Study tip: For HESI geometry problems, always identify what each term in a formula represents before substituting. With surface area formulas especially, make sure you're accounting for all surfaces — tops, bottoms, and sides. Write out each component separately to avoid missing parts of composite shapes.
A nurse calculates fluid replacement using the formula $F = 25m + 40(t - 2)$ , where $F$ is fluid in mL, $m$ is patient mass in kg, and $t$ is time since admission in hours. For a 68 kg patient who has been admitted for 5 hours, what is the required fluid replacement?
Answer: 1820 mL from the given formula Substituting $m = 68$ and $t = 5$ : $F = 25(68) + 40(5 - 2) = 1700 + 40(3) = 1700 + 120 = 1820$ mL. Choice A incorrectly calculates $40(5-2)$ as $40(2) = 80$ . Choice B stops the calculation at $25(68) = 1700$ without adding the time component. Choice D incorrectly calculates the time component as $40(5) = 200$ instead of $40(3) = 120$ .
Insulin dosage is determined by $I = 0.5g + 3(m - 5)$ where $g$ is glucose level in mg/dL above 100, and $m$ is meal carbohydrate content in units of 10g. If glucose level is 180 mg/dL and the meal contains 80g of carbohydrates, what is the insulin dosage?
Answer: 49 units from proper formula First, $g = 180 - 100 = 80$ mg/dL above 100. Then $m = 80 ÷ 10 = 8$ units of 10g. Substituting: $I = 0.5(80) + 3(8 - 5) = 40 + 3(3) = 40 + 9 = 49$ units. Choice A incorrectly omits the meal component. Choice C incorrectly calculates $m$ as the raw carbohydrate value (80) instead of units of 10g. Choice D incorrectly adds rather than subtracts 5 from $m$ .

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